# lightkurve.correctors.RegressionCorrector#

class lightkurve.correctors.RegressionCorrector(lc)[source]#

Remove noise using linear regression against a DesignMatrix.

$\newcommand{\y}{\mathbf{y}} \newcommand{\cov}{\boldsymbol\Sigma_\y} \newcommand{\w}{\mathbf{w}} \newcommand{\covw}{\boldsymbol\Sigma_\w} \newcommand{\muw}{\boldsymbol\mu_\w} \newcommand{\sigw}{\boldsymbol\sigma_\w} \newcommand{\varw}{\boldsymbol\sigma^2_\w}$

Given a column vector of data $$\y$$ and a design matrix of regressors $$X$$, we will find the vector of coefficients $$\w$$ such that:

$\mathbf{y} = X\mathbf{w} + \mathrm{noise}$

We will assume that the model fits the data within Gaussian uncertainties:

$p(\y | \w) = \mathcal{N}(X\w, \cov)$

We make the regression robust by placing Gaussian priors on $$\w$$:

$p(\w) = \mathcal{N}(\muw, \sigw)$

We can then find the maximum likelihood solution of the posterior distribution $$p(\w | \y) \propto p(\y | \w) p(\w)$$ by solving the matrix equation:

$\begin{split}\w = \covw (X^\\top \cov^{-1} \y + \\boldsymbol\sigma^{-2}_\w I \muw)\end{split}$

Where $$\covw$$ is the covariance matrix of the coefficients:

$\begin{split}\covw^{-1} = (X^\\top \cov^{-1} X + \\boldsymbol\sigma^{-2}_\w I)\end{split}$
Parameters
lcLightCurve

The light curve that needs to be corrected.

__init__(lc)[source]#

Constructor method.

The constructor shall:

• accept all data required to run the correction (e.g. light curves, target pixel files, engineering data).

• instantiate the original_lc property.

Methods

 Constructor method. compute_overfit_metric(**kwargs) Measures the degree of over-fitting in the correction. compute_underfit_metric(**kwargs) Measures the degree of under-fitting the correction. correct(design_matrix_collection[, ...]) Find the best fit correction for the light curve. Returns diagnostic plots to assess the most recent call to correct(). diagnose_priors() Returns a diagnostic plot visualizing how the best-fit coefficients compare against the priors.

Attributes

 cadence_mask corrected_lc dmc Shorthand for self.design_matrix_collection. original_lc